# arXiv daily: Populations and Evolution (q-bio.PE)

##### 1.Branching model with state dependent offspring distribution for Chlamydia spread

**Authors:**Péter Kevei, Máté Szalai

**Abstract:** Chlamydiae are bacteria with an interesting unusual developmental cycle. A single bacterium in its infectious form (elementary body, EB) enters the host cell, where it converts into its dividing form (reticulate body, RB), and divides by binary fission. Since only the EB form is infectious, before the host cell dies, RBs start to convert into EBs. After the host cell dies RBs do not survive. We model the population growth by a 2-type discrete-time branching process, where the probability of duplication depends on the state. Maximizing the EB production leads to a stochastic optimization problem. Simulation study shows that our novel model is able to reproduce the main features of the development of the population.

##### 1.Theory for Adaptive Systems: Collective Robustness of Genotype-Phenotype Evolution

**Authors:**Tuan Minh Pham, Kunihiko Kaneko

**Abstract:** The investigation of mutually coupled dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding biological evolution and learning. We develop a general theory for such dynamics by extending dynamical mean field theory. We then apply our framework to biological systems whose fate is determined by the evolution of genotype-phenotype relationship. Here phenotypic evolution is shaped by stochastic gene-expression fast dynamics and is coupled to selection-based slow changes of genotypes encoding the network of gene regulations. We find dynamically robust patterns of phenotypes can be achieved under an intermediate level of external noise where the genotype-phenotype relation evolves in such a way that results in intrinsic out-of-equilibrium fluctuations of phenotypes even in the absence of that noise.

##### 1.Muller's ratchet in a near-critical regime: tournament versus fitness proportional selection

**Authors:**Jan Lukas Igelbrink, Adrián González Casanova, Charline Smadi, Anton Wakolbinger

**Abstract:** Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. The classical variant considers {\it fitness proportional} selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. ([EPW09]) we propose a parameter scaling which fits well to the ``near-critical'' regime that was in the focus of [EPW09] (and in which the mutation-selection ratio diverges logarithmically as $N\to \infty$). Using a Moran model, we investigate the``rule of thumb'' given in [EPW09] for the click rate of the ``classical ratchet'' by putting it into the context of new results on the long-time evolution of the size of the best class of the ratchet with (binary) tournament selection, which (other than that of the classical ratchet) follows an autonomous dynamics up to the time of its extinction. In [GSW23] it was discovered that the tournament ratchet has a hierarchy of dual processes which can be constructed on top of an Ancestral Selection graph with a Poisson decoration. For a regime in which the mutation/selection-ratio remains bounded away from 1, this was used in [GSW23] to reveal the asymptotics of the click rates as well as that of the type frequency profile between clicks. We will describe how these ideas can be extended to the near-critical regime in which the mutation-selection ratio of the tournament ratchet converges to 1 as $N\to \infty$.

##### 2.Digital contact tracing/notification for SARS-CoV-2: a retrospective of what went wrong

**Authors:**Joanna Masel, James Petrie, Jason Bay, Wolfgang Ebbers, Aalekh Sharan, Scott Leibrand, Andreas Gebhard, Samuel Zimmerman

**Abstract:** Digital contact tracing/notification was initially hailed as a promising strategy to combat SARS-CoV-2, but in most jurisdictions it did not live up to its promise. To avert a given transmission event, both parties must have adopted the tech, it must detect the contact, the primary case must be promptly diagnosed, notifications must be triggered, and the secondary case must change their behavior to avoid the focal tertiary transmission event. Achieving a 26% reduction in R(t) requires 80% success rates at each of these six points of failure. Here we review the six failure rates experienced by a variety of digital contact tracing/notification schemes, including Singapore's TraceTogether, India's Aarogya Setu, and leading implementations of the Google Apple Exposure Notification system. This leads to a number of recommendations, e.g. that tracing/notification apps be multi-functional and integrated with testing, manual contact tracing, and the gathering of critical scientific data, and that the narrative be framed in terms of user autonomy rather than user privacy.

##### 1.Wind turbine power and land cover effects on cumulative bat deaths

**Authors:**Aristides Moustakas, Panagiotis Georgiakakis, Elzbieta Kret, Eleftherios Kapsalis

**Abstract:** Wind turbines (WT) cause bird and bat mortalities which depend on the WT and landscape features. The effects of WT features and environmental variables at different spatial scales associated to bat deaths in a mountainous and forested area in Thrace, NE Greece were investigated. Initially, we sought to quantify the most lethal WT characteristic between tower height, rotor diameter and power. The scale of interaction distance between bat deaths and the land cover characteristics surrounding the WTs was quantified. A statistical model was trained and validated against bat deaths and WT, land cover and topography features. Variance partitioning between bat deaths and the explanatory covariates was conducted. The trained model was used to predict bat deaths attributed to existing and future wind farm development in the region. Results indicated that the optimal interaction distance between WT and surrounding land cover was 5 km, the larger distance than the ones examined. WT power, natural land cover type and distance from water explained 40 %, 15 % and 11 % respectively of the total variance in bat deaths by WTs. The model predicted that operating but not surveyed WTs comprise of 377.8% and licensed but not operating yet will contribute to 210.2% additional deaths than the ones recorded. Results indicate that among all WT features and land cover characteristics, wind turbine power is the most significant factor associated to bat deaths. Results indicated that WTs located within 5 km buffer comprised of natural land cover types have substantial higher deaths. More WT power will result in more deaths. Wind turbines should not be licensed in areas where natural land cover at a radius of 5km exceeds 50%. These results are discussed in the climate-land use-biodiversity-energy nexus.

##### 2.Steady-state analysis of networked epidemic models

**Authors:**Sei Zhen Khong, Lanlan Su

**Abstract:** Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two positive feedback frameworks that are applicable to the study of steady-state values in a wide range of compartmental epidemic models, including both group and networked processes. In the case of a group (resp. networked) model, we show that the convergence limit of the susceptible proportion of the population (resp. the susceptible proportion in at least one of the subgroups) is upper bounded by the reciprocal of the basic reproduction number (BRN) of the model. The BRN, when it is greater than unity, thus demonstrates the level of penetration into a subpopulation by the disease. Both non-strict and strict bounds on the convergence limits are derived and shown to correspond to substantially distinct scenarios in the epidemic processes, one in the presence of the endemic state and another without. Formulae for calculating the limits are provided in the latter case. We apply the developed framework to examining various group and networked epidemic models commonly seen in the literature to verify the validity of our conclusions.

##### 3.Closed ecosystems extract energy through self-organized nutrient cycles

**Authors:**Akshit Goyal, Avi I. Flamholz, Alexander P. Petroff, Arvind Murugan

**Abstract:** Our planet is roughly closed to matter, but open to energy input from the sun. However, to harness this energy, organisms must transform matter from one chemical (redox) state to another. For example, photosynthetic organisms can capture light energy by carrying out a pair of electron donor and acceptor transformations (e.g., water to oxygen, CO$_2$ to organic carbon). Closure of ecosystems to matter requires that all such transformations are ultimately balanced, i.e., other organisms must carry out corresponding reverse transformations, resulting in cycles that are coupled to each other. A sustainable closed ecosystem thus requires self-organized cycles of matter, in which every transformation has sufficient thermodynamic favorability to maintain an adequate number of organisms carrying out that process. Here, we propose a new conceptual model that explains the self-organization and emergent features of closed ecosystems. We study this model with varying levels of metabolic diversity and energy input, finding that several thermodynamic features converge across ecosystems. Specifically, irrespective of their species composition, large and metabolically diverse communities self-organize to extract roughly 10% of the maximum extractable energy, or 100 fold more than randomized communities. Moreover, distinct communities implement energy extraction in convergent ways, as indicated by strongly correlated fluxes through nutrient cycles. As the driving force from light increases, however, these features -- fluxes and total energy extraction -- become more variable across communities, indicating that energy limitation imposes tight thermodynamic constraints on collective metabolism.

##### 4.Species interactions reproduce abundance correlations patterns in microbial communities

**Authors:**José Camacho-Mateu, Aniello Lampo, Matteo Sireci, Miguel Ángel Muñoz, José A. Cuesta

**Abstract:** During the last decades macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations over metagenomic samples are found to be correlated, but reproducing populations through appropriate population models remains still an open task. The present paper tackles this problem and points to species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka-Volterra constants as successful ansatz. We design a Bayesian inference algorithm to obtain sets of interaction constants able to reproduce the experimental correlation distributions much better than the state-of-the-art attempts. Importantly, the model still reproduces single-species, experimental, macroecological patterns previously detected in the literature, concerning the abundance fluctuations across both species and communities. Endorsed by the agreement with the observed phenomenology, our analysis provides insights on the properties of microbial interactions, and suggests their sparsity as a necessary feature to balance the emergence of different patterns.

##### 1.Scaling symmetries and parameter reduction in epidemic SI(R)S models

**Authors:**Florian Nill

**Abstract:** Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group G, parameter space A becomes a (locally) trivial principal bundle, A ~ A/G x G, then the normalized dynamics only depends on the quotient A/G. In this way, the dynamics of fractional variables in homogeneous epidemic SI(R)S models, with standard incidence, absence of R-susceptibility and compartment independent birth and death rates, turns out to be isomorphic to (a marginally extended version of) Hethcote's classic endemic model, first presented in 1973. The paper studies a 10-parameter master model with constant and I-linear vaccination rates, vertical transmission and a vaccination rate for susceptible newborns. As recently shown by the author, all demographic parameters are redundant. After adjusting time scale, the remaining 5-parameter model admits a 3-dimensional abelian scaling symmetry. By normalization we end up with Hethcote's extended 2-parameter model. Thus, in view of symmetry concepts, reproving theorems on endemic bifurcation and stability in such models becomes needless.

##### 1.Fractional model of COVID--19 with pathogens as shedding effects

**Authors:**Faïçal Ndaïrou, Moein Khalighi, Leo Lahti

**Abstract:** To develop effective strategies for controlling the spread of the virus and potential future outbreaks, a deep understanding of disease transmission dynamics is crucial. This study proposes a modification to existing mathematical models used to describe the transmission dynamics of COVID-19 with environmental pathogens, incorporating a variable population, and employing incommensurate fractional order derivatives in ordinary differential equations. Our analysis accurately computes the basic reproduction number and demonstrates the global stability of the disease-free equilibrium point. Numerical simulations fitted to real data from South Africa show the efficacy of our proposed model, with fractional models enhancing flexibility. We also provide reliable values for initial conditions, model parameters, and order derivatives, and examine the sensitivity of model parameters. Our study provides valuable insights into COVID-19 transmission dynamics and has the potential to inform the development of effective control measures and prevention strategies.

##### 2.Image background assessment as a novel technique for insect microhabitat identification

**Authors:**Sesa Singha Roy, Reid Tingley, Alan Dorin

**Abstract:** The effects of climate change, urbanisation and agriculture are changing the way insects occupy habitats. Some species may utilise anthropogenic microhabitat features for their existence, either because they prefer them to natural features, or because of no choice. Other species are dependent on natural microhabitats. Identifying and analysing these insects' use of natural and anthropogenic microhabitats is important to assess their responses to a changing environment, for improving pollination and managing invasive pests. Traditional studies of insect microhabitat use can now be supplemented by machine learning-based insect image analysis. Typically, research has focused on automatic insect classification, but valuable data in image backgrounds has been ignored. In this research, we analysed the image backgrounds available on the ALA database to determine their microhabitats. We analysed the microhabitats of three insect species common across Australia: Drone flies, European honeybees and European wasps. Image backgrounds were classified as natural or anthropogenic microhabitats using computer vision and machine learning tools benchmarked against a manual classification algorithm. We found flies and honeybees in natural microhabitats, confirming their need for natural havens within cities. Wasps were commonly seen in anthropogenic microhabitats. Results show these insects are well adapted to survive in cities. Management of this invasive pest requires a thoughtful reduction of their access to human-provided resources. The assessment of insect image backgrounds is instructive to document the use of microhabitats by insects. The method offers insight that is increasingly vital for biodiversity management as urbanisation continues to encroach on natural ecosystems and we must consciously provide resources within built environments to maintain insect biodiversity and manage invasive pests.

##### 1.Information encoded in gene-frequency trajectories

**Authors:**Konstantinos Mavreas, David Waxman

**Abstract:** In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded in gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard result for the probability of fixation, under the diffusion approximation, systematically emerges, when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

##### 1.A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals

**Authors:**Fabio A. C. C. Chalub, Antonio Gómez-Corral, Martín López-García, Fátima Palacios-Rodríguez

**Abstract:** This paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. The aim is to determine the probability law of the exact reproduction number Rexact,0 which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number Rexact,0 into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods.

##### 1.Dynamics of niche construction in adaptable populations evolving in diverse environments

**Authors:**Eleni Nisioti, Clément Moulin-Frier

**Abstract:** In both natural and artificial studies, evolution is often seen as synonymous to natural selection. Individuals evolve under pressures set by environments that are either reset or do not carry over significant changes from previous generations. Thus, niche construction (NC), the reciprocal process to natural selection where individuals incur inheritable changes to their environment, is ignored. Arguably due to this lack of study, the dynamics of NC are today little understood, especially in real-world settings. In this work, we study NC in simulation environments that consist of multiple, diverse niches and populations that evolve their plasticity, evolvability and niche-constructing behaviors. Our empirical analysis reveals many interesting dynamics, with populations experiencing mass extinctions, arms races and oscillations. To understand these behaviors, we analyze the interaction between NC and adaptability and the effect of NC on the population's genomic diversity and dispersal, observing that NC diversifies niches. Our study suggests that complexifying the simulation environments studying NC, by considering multiple and diverse niches, is necessary for understanding its dynamics and can lend testable hypotheses to future studies of both natural and artificial systems.

##### 1.Spatial patterns and biodiversity in rock-paper-scissors models with regional unevenness

**Authors:**J. Menezes, M. Tenorio

**Abstract:** Climate changes may affect ecosystems destabilising relationships among species. We investigate the spatial rock-paper-scissors models with a regional unevenness that reduces the selection capacity of organisms of one species. Our results show that the regionally weak species predominates in the local ecosystem, while spiral patterns appear far from the region, where individuals of every species play the rock-paper-scissors game with the same strength. Because the weak species controls all local territory, it is attractive for the other species to enter the local ecosystem to conquer the territory. However, our stochastic simulations show that the transitory waves formed when organisms of the strong species reach the region are quickly destroyed because of local strength unbalance in the selection game rules. Computing the effect of the topology on population dynamics, we find that the prevalence of the weak species becomes more significant if the transition of the selection capacity to the area of uneven rock-paper-scissors rules is smooth. Finally, our findings show that the biodiversity loss due to the arising of regional unevenness is minimised if the transition to the region where the cyclic game is unbalanced is abrupt. Our results may be helpful to biologists in comprehending the consequences of changes in the environmental conditions on species coexistence and spatial patterns in complex systems.

##### 1.Modelling disease impact: lifespan reduction is greatest for young adults in an exogenous damage model of disease

**Authors:**Rebecca Tobin, Glen Pridham, Andrew D. Rutenberg

**Abstract:** We model the effects of disease and other exogenous damage during human aging. While the exogenous damage is repaired at the end of acute disease, propagated secondary damage remains. We consider both short-term mortality effects due to (acute) exogenous damage and long-term mortality effects due to propagated damage within the context of a generic network model (GNM) of individual aging. Across a wide range of disease durations and severities we find that while excess short-term mortality is highest for the oldest individuals, the long-term years of life lost are highest for the youngest individuals. These appear to be universal effects of human disease. We support this conclusion with a phenomenological model coupling damage and mortality. Our results are qualitatively consistent with existing observational studies, though these are mostly limited to short time-horizons. Short-time horizon studies may have significant limitations for understanding the lifetime impacts of disease on both individuals and populations.

##### 1.A Chip-Firing Game for Biocrust Reverse Succession

**Authors:**Shloka V. Janapaty

**Abstract:** Experimental work suggests that biological soil crusts, dominant primary producers in drylands and tundra, are particularly vulnerable to disturbances that cause reverse ecological succession. To model successional transitions in biocrust communities, we propose a resource-firing game that captures succession dynamics without specifying detailed function forms. The model is evaluated in idealized terrestrial ecosystems, where disturbances are modeled as a reduction in available resources that triggers inter-species competition. The resource-firing game is executed on a finite graph with nodes representing species in the community and a sink node that becomes active when every species is depleted of resources. First, we discuss the theoretical basis of the resource-firing game, evaluate it in the light of existing literature, and consider the characteristics of a biocrust community that has evolved to equilibrium. We then examine the dependence of resource-firing and game stability on species richness, showing that high species richness increases the probability of very short and long avalanches, but not those of intermediate length. Indeed, this result suggests that the response of the community to disturbance is both directional and episodic, proceeding towards reverse succession in bursts of variable length. Finally, we incorporate the spatial structure of the biocrust community into a Cayley Tree and derive a formula for the probability that a disturbance, modeled as a random attack, initiates a large species-death event.

##### 2.Cell lineage statistics with incomplete population trees

**Authors:**Arthur Genthon, Takashi Nozoe, Luca Peliti, David Lacoste

**Abstract:** Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete lineages that do not survive until the end of the experiment? Here, we develop a model-independent theoretical framework to address this issue. We show how to quantify fitness landscape, survivor bias and selection for arbitrary cell traits from cell lineage statistics in the presence of death, and we test this method using an experimental data set in which a cell population is exposed to a drug that kills a large fraction of the population. This analysis reveals that failing to properly account for dead lineages can lead to misleading fitness estimations. For simple trait dynamics, we prove and illustrate numerically that the fitness landscape and the survivor bias can in addition be used for the non-parametric estimation of the division and death rates, using only lineage histories. Our framework provides universal bounds on the population growth rate, and a fluctuation-response relation which quantifies the reduction of population growth rate due to the variability in death rate. Further, in the context of cell size control, we obtain generalizations of Powell's relation that link the distributions of generation times with the population growth rate, and show that the survivor bias can sometimes conceal the adder property, namely the constant increment of volume between birth and division.

##### 1.Biophysical Cybernetics of Directed Evolution and Eco-evolutionary Dynamics

**Authors:**Bryce Allen Bagley

**Abstract:** Many major questions in the theory of evolutionary dynamics can in a meaningful sense be mapped to analyses of stochastic trajectories in game theoretic contexts. Often the approach is to analyze small numbers of distinct populations and/or to assume dynamics occur within a regime of population sizes large enough that deterministic trajectories are an excellent approximation of reality. The addition of ecological factors, termed "eco-evolutionary dynamics", further complicates the dynamics and results in many problems which are intractable or impractically messy for current theoretical methods. However, an analogous but underexplored approach is to analyze these systems with an eye primarily towards uncertainty in the models themselves. In the language of researchers in Reinforcement Learning and adjacent fields, a Partially Observable Markov Process. Here we introduce a duality which maps the complexity of accounting for both ecology and individual genotypic/phenotypic types onto a problem of accounting solely for underlying information-theoretic computations rather than drawing physical boundaries which do not change the computations. Armed with this equivalence between computation and the relevant biophysics, which we term Taak-duality, we attack the problem of "directed evolution" in the form of a Partially Observable Markov Decision Process. This provides a tractable case of studying eco-evolutionary trajectories of a highly general type, and of analyzing questions of potential limits on the efficiency of evolution in the directed case.

##### 1.The Role of Quarantine and Isolation in Controlling COVID-19 Hospitalization in Oman

**Authors:**Maryam Al-Yahyai
Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman, Fatma Al-Musalhi
Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman, Nasser Al-Salti
Department of Applied Mathematics and Science, National University of Science and Technology, Muscat, Oman, Ibrahim Elmojtaba
Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman

**Abstract:** In this paper, we build a mathematical model for the dynamics of COVID-19 to assess the impact of placing healthy individuals in quarantine and isolating infected ones on the number of hospitalization and intensive care unit cases. The proposed model is fully analyzed in order to prove the positivity of solutions, to study the local and global stability of the disease-free equilibria and to drive the basic and control reproduction numbers of the model. Oman COVID-19 data is used to calibrate the model and estimate the parameters. In particular, the published data for the year 2020 is used, when two waves of the disease hit the country. Moreover, this period of time is chosen when no vaccine had been introduced, but only the non-pharmaceutical intervention (NPI) strategies were the only effective methods to control the spread and, consequently, control the hospitalization cases to avoid pressuring the health system. Based on the estimated parameters, the reproduction number and contribution of different transmission routes are approximated numerically. Sensitivity analysis is performed to identify the significant parameters in spreading the disease. Numerical simulation is carried out to demonstrate the effects of quarantine and isolation on the number of hospitalized cases.

##### 1.Multi-Species Prey-Predator Dynamics During a Multi-Strain Pandemic

**Authors:**Ariel Alexi, Ariel Rosenfeld, Teddy Lazebnik

**Abstract:** Small and large scale pandemics are a natural phenomenon repeatably appearing throughout history, causing ecological and biological shifts in ecosystems and a wide range of their habitats. These pandemics usually start with a single strain but shortly become multi-strain due to a mutation process of the pathogen causing the epidemic. In this study, we propose a novel eco-epidemiological model that captures multi-species prey-predator dynamics with a multi-strain pandemic. The proposed model extends and combines the Lotka-Volterra prey-predator model and the Susceptible-Infectious-Recovered (SIR) epidemiological model. We investigate the ecosystem's sensitivity and stability during such a multi-strain pandemic through extensive simulation relying on both synthetic cases as well as two real-world configurations. Our results are aligned with known ecological and epidemiological findings, thus supporting the adequacy of the proposed model in realistically capturing the complex eco-epidemiological properties of the multi-species multi-strain pandemic dynamics.

##### 1.Directionality Theory and the Origin of Life

**Authors:**Lloyd Demetrius

**Abstract:** The origin of cellular life can be described in terms of the transition from inorganic matter: solids, liquids and gases, to the emergence of cooperative assemblies of organic matter, DNA and proteins,capable of replication and metabolism. Directionality Theory is a mathematical model of the collective behavior of populations of organic matter: cells and higher organisms. Evolutionary entropy, the cornerstone of the theory, is a statistical measure of the cooperativity of the interacting components that comprise the population. The main tenet of Directionality Theory is the Entropic Principle of Collective Behavior: The collective behavior of aggregates of organic matter is contingent on the population size and the external energy source, and characterized by extremal states of evolutionary entropy. This article invokes Directionality Theory to provide an evolutionary rationale for the following sequence of transformations which define the emergence of cellular life: 1. The self-assembly of activated macromolecules from inorganic matter 2. The emergence of an RNA world, defined by RNA molecules with catalytic and replicative properties 3. The origin of cellular life, the integration of the three carbon-based polymers: DNA, proteins and lipids, to generate a metabolic and replicative unit.

##### 1.Phylo2Vec: a vector representation for binary trees

**Authors:**Matthew J Penn, Neil Scheidwasser, Mark P Khurana, David A Duchêne, Christl A Donnelly, Samir Bhatt

**Abstract:** Binary phylogenetic trees inferred from biological data are central to understanding the shared evolutionary history of organisms. Inferring the placement of latent nodes in a tree by any optimality criterion (e.g., maximum likelihood) is an NP-hard problem, propelling the development of myriad heuristic approaches. Yet, these heuristics often lack a systematic means of uniformly sampling random trees or effectively exploring a tree space that grows factorially, which are crucial to optimisation problems such as machine learning. Accordingly, we present Phylo2Vec, a new parsimonious representation of a phylogenetic tree. Phylo2Vec maps any binary tree with $n$ leaves to an integer vector of length $n$. We prove that Phylo2Vec is both well-defined and bijective to the space of phylogenetic trees. The advantages of Phylo2Vec are twofold: i) easy uniform sampling of binary trees and ii) systematic ability to traverse tree space in very large or small jumps. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets and show that a simple hill climbing-based optimisation efficiently traverses the vastness of tree space from a random to an optimal tree.

##### 2.Revising the global biogeography of plant life cycles

**Authors:**Tyler Poppenwimer, Itay Mayrose, Niv DeMalach

**Abstract:** There are two main life cycles in plants, annual and perennial. These life cycles are associated with different traits, which determine ecosystem function. Although life cycles are textbook examples of plant adaptation to different environments, we lack comprehensive knowledge regarding global distributional patterns. Here, we assembled an extensive database of plant life cycle assignments of 235,000 plant species coupled with millions of georeferenced datapoints to map the worldwide biogeography of life cycles. We found that annuals are half as common as initially thought, accounting for only 6% of species. Our analyses indicate annuals are favored in hot and dry regions. However, a more accurate model shows annual species' prevalence is driven by temperature and precipitation in the driest quarter (rather than yearly means), explaining, for example, why some Mediterranean systems have more annuals than deserts. Furthermore, this pattern remains consistent among different families, indicating convergent evolution. Finally, we demonstrate that increasing climate variability and anthropogenic disturbance increase annual favorability. Considering future climate change, we predict an increase in annual prevalence for 81% of the world's ecoregions by 2100. Overall, our analyses raise concerns for ecosystem services provided by perennials as ongoing changes are leading to a more annuals-dominated world.

##### 1.The Theory of Gene Family Histories

**Authors:**Marc Hellmuth, Peter F. Stadler

**Abstract:** Most genes are part of larger families of evolutionary related genes. The history of gene families typically involves duplications and losses of genes as well as horizontal transfers into other organisms. The reconstruction of detailed gene family histories, i.e., the precise dating of evolutionary events relative to phylogenetic tree of the underlying species has remained a challenging topic despite their importance as a basis for detailed investigations into adaptation and functional evolution of individual members of the gene family. The identification of orthologs, moreover, is a particularly important subproblem of the more general setting considered here. In the last few years, an extensive body of mathematical results has appeared that tightly links orthology, a formal notion of best matches among genes, and horizontal gene transfer. The purpose of this chapter is the broadly outline some of the key mathematical insights and to discuss their implication for practical applications. In particular, we focus on tree-free methods, i.e., methods to infer orthology or horizontal gene transfer as well as gene trees, species trees and reconciliations between them without using \emph{a priori} knowledge of the underlying trees or statistical models for the inference of phylogenetic trees. Instead, the initial step aims to extract binary relations among genes.

##### 2.Reporting delays: a widely neglected impact factor in COVID-19 forecasts

**Authors:**Long MA, Piet Van Mieghem, Maksim Kitsak

**Abstract:** Epidemic forecasts are only as good as the accuracy of epidemic measurements. Is epidemic data, particularly COVID-19 epidemic data, clean and devoid of noise? Common sense implies the negative answer. While we cannot evaluate the cleanliness of the COVID-19 epidemic data in a holistic fashion, we can assess the data for the presence of reporting delays. In our work, through the analysis of the first COVID-19 wave, we find substantial reporting delays in the published epidemic data. Motivated by the desire to enhance epidemic forecasts, we develop a statistical framework to detect, uncover, and remove reporting delays in the infectious, recovered, and deceased epidemic time series. Our framework can uncover and analyze reporting delays in 8 regions significantly affected by the first COVID-19 wave. Further, we demonstrate that removing reporting delays from epidemic data using our statistical framework may decrease the error in epidemic forecasts. While our statistical framework can be used in combination with any epidemic forecast method that intakes infectious, recovered, and deceased data, to make a basic assessment, we employed the classical SIRD epidemic model. Our results indicate that the removal of reporting delays from the epidemic data may decrease the forecast error by up to 50. We anticipate that our framework will be indispensable in the analysis of novel COVID-19 strains and other existing or novel infectious diseases.

##### 1.Evolutionary stability of antigenically escaping viruses

**Authors:**Victor Chardès, Andrea Mazzolini, Thierry Mora, Aleksandra M. Walczak

**Abstract:** Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the co-evolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other non-antigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of non-antigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

##### 1.A discrete model for the growth and spread of the Scottish populations of red squirrels (Sciurus vulgaris) and grey squirrels (Sciurus carolinensis)

**Authors:**Jean-Baptiste Gramain

**Abstract:** In this article, a model, discrete in space and time, is developed to describe the growth and spread of the Scottish populations of red squirrels (Sciurus vulgaris) and grey squirrel (Sciurus carolinensis). The initial state for the model is designed using a large dataset of records of sightings of individuals of both species reported by members of the public. Choices of parameters involved in the model and their values are informed by the analysis of this dataset for the period 2011-2016, and model predictions are compared to records for the years 2006-2019.

##### 1.Exact solutions for diffusive transport on heterogeneous growing domains

**Authors:**Stuart T. Johnston, Matthew J. Simpson

**Abstract:** From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely employed to investigate diffusive processes on growing domains. However, a standard assumption is that the domain growth is spatially uniform. There are many relevant examples where this is not the case, such as the colonisation of growing gut tissue by neural crest cells. As such, it is not straightforward to disentangle the individual roles of heterogeneous growth and diffusive transport. Here we present exact solutions to models of diffusive transport on domains undergoing spatially non-uniform growth. The exact solutions are obtained via a combination of transformation, convolution and superposition techniques. We verify the accuracy of these solutions via comparison with simulations of a corresponding lattice-based random walk. We explore various domain growth functions, including linear growth, exponential growth and contraction, and oscillatory growth. Provided the domain size remains positive, we find that the derived solutions are valid. The exact solutions reveal the relationship between model parameters, such as the diffusivity and the type and rate of domain growth, and key statistics, such as the survival and splitting probabilities.

##### 2.A model for seagrass species competition: dynamics of the symmetric case

**Authors:**Pablo Moreno-Spiegelberg, Damià Gomila

**Abstract:** We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between species through the net mortality rate. We consider both intraspecies and interspecies facilitative and competitive interactions, allowing density-dependent interaction mechanisms. Here we study the case of very similar species with reciprocal interactions, which allows reducing the number of the model parameters to just four, and whose bifurcation structure can be considered the backbone of the complete system. We find that the parameter space can be divided into ten regions with qualitatively different bifurcation diagrams. These regimes can be further grouped into just five regimes with different ecological interpretations. Our analysis allows the classifying of all possible density distributions and dynamical behaviors of meadows with two coexisting species.

##### 3.Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations

**Authors:**Diogo L. Pires, Igor Erovenko, Mark Broom

**Abstract:** Evolutionary models are used to study the self-organisation of collective action, often incorporating population structure due to its ubiquitous presence and long-known impact on emerging phenomena. We investigate the evolution of multiplayer cooperation in mobile structured populations, where individuals move strategically on networks and interact with those they meet in groups of variable size. We find that the evolution of multiplayer cooperation primarily depends on the network topology and movement cost while using different stochastic update rules seldom influences evolutionary outcomes. Cooperation robustly co-evolves with movement on complete networks and structure has a partially detrimental effect on it. These findings contrast an established wisdom in evolutionary graph theory that cooperation can only emerge under some update rules and if the average degree is low. We find that group-dependent movement erases the locality of interactions, suppresses the impact of evolutionary structural viscosity on the fitness of individuals, and leads to assortative behaviour that is much more powerful than viscosity in promoting cooperation. We analyse the differences remaining between update rules through a comparison of evolutionary outcomes and fixation probabilities.

##### 1.Playing it safe: information constrains collective betting strategies

**Authors:**Philipp Fleig, Vijay Balasubramanian

**Abstract:** Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or explicitly involves the assumption of a model of the world. Better information about environmental statistics can improve the bet quality, but in practice resources for information gathering are always limited. We argue that theories of optimal inference dictate that ``complex'' models are harder to infer with bounded information and lead to larger prediction errors. Thus, we propose a principle of ``playing it safe'' where, given finite information gathering capacity, biological systems should be biased towards simpler models of the world, and thereby to less risky betting strategies. In the framework of Bayesian inference, we show that there is an optimally safe adaptation strategy determined by the Bayesian prior. We then demonstrate that, in the context of stochastic phenotypic switching by bacteria, implementation of our principle of ``playing it safe'' increases fitness (population growth rate) of the bacterial collective. We suggest that the principle applies broadly to problems of adaptation, learning and evolution, and illuminates the types of environments in which organisms are able to thrive.

##### 2.Robustness and complexity

**Authors:**Steven A. Frank

**Abstract:** When a biological system robustly corrects component-level errors, the direct pressure on component performance declines. Components may become less reliable, maintain more genetic variability, or drift neutrally in design, creating the basis for new forms of organismal complexity. This article links the protection-decay dynamic to other aspects of robust and complex systems. Examples include the hourglass pattern of biological development and Doyle's hourglass architecture for robustly complex systems in engineering. The deeply and densely connected wiring architecture in biology's cellular controls and in machine learning's computational neural networks provide another link. By unifying these seemingly different aspects into a unified framework, we gain a new perspective on robust and complex systems.

##### 1.Back to the future: a simplified and intuitive derivation of the Lotka-Euler equation

**Authors:**Carlos Hernandez-Suarez

**Abstract:** The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which $N$ individuals produce their offspring, resulting in a population size of $N R_0$, where $R_0$ is the average offspring size. It is essentially a birth process, and here it is shown that by reversing the process to a death process, in which $N R_0$ individuals die at a rate $\lambda^{-1}$, the derivation of the Lotka-Euler equation becomes more intuitive and direct, both in discrete and continuous time.

##### 1.Bayesian mixture models for phylogenetic source attribution from consensus sequences and time since infection estimates

**Authors:**Alexandra Blenkinsop, Lysandros Sofocleous, Francesco di Lauro, Evangelia Georgia Kostaki, Ard van Sighem, Daniela Bezemer, Thijs van de Laar, Peter Reiss, Godelieve de Bree, Nikos Pantazis, Oliver Ratmann

**Abstract:** In stopping the spread of infectious diseases, pathogen genomic data can be used to reconstruct transmission events and characterize population-level sources of infection. Most approaches for identifying transmission pairs do not account for the time that passed since divergence of pathogen variants in individuals, which is problematic in viruses with high within-host evolutionary rates. This is prompting us to consider possible transmission pairs in terms of phylogenetic data and additional estimates of time since infection derived from clinical biomarkers. We develop Bayesian mixture models with an evolutionary clock as signal component and additional mixed effects or covariate random functions describing the mixing weights to classify potential pairs into likely and unlikely transmission pairs. We demonstrate that although sources cannot be identified at the individual level with certainty, even with the additional data on time elapsed, inferences into the population-level sources of transmission are possible, and more accurate than using only phylogenetic data without time since infection estimates. We apply the approach to estimate age-specific sources of HIV infection in Amsterdam MSM transmission networks between 2010-2021. This study demonstrates that infection time estimates provide informative data to characterize transmission sources, and shows how phylogenetic source attribution can then be done with multi-dimensional mixture models.

##### 2.Fire responses shape plant communities in a minimal model for fire ecosystems across the world

**Authors:**Marta Magnani, Rubén Díaz-Sierra, Luke Sweeney, Antonello Provenzale, Mara Baudena

**Abstract:** Across plant communities worldwide, fire regimes reflect a combination of climatic factors and plant characteristics. To shed new light on the complex relationships between plant characteristics and fire regimes, we developed a new conceptual, mechanistic model that includes plant competition, stochastic fires, and fire-vegetation feedback. Considering a single standing plant functional type, we observed that highly flammable and slowly colonizing plants can persist only when they have a strong fire response, while fast colonizing and less flammable plants can display a larger range of fire responses. At the community level, the fire response of the strongest competitor determines the existence of alternative ecological states, i.e. different plant communities, under the same environmental conditions. Specifically, when the strongest competitor had a very strong fire response, such as in Mediterranean forests, only one ecological state could be achieved. Conversely, when the strongest competitor was poorly fire-adapted, alternative ecological states emerged, for example between tropical humid savannas and forests, or between different types of boreal forests. These findings underline the importance of including the plant fire response when modeling fire ecosystems, e.g. to predict the vegetation response to invasive species or to climate change.

##### 3.Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks

**Authors:**Wajid Ali, Christopher E. Overton, Robert R. Wilkinson, Kieran J. Sharkey

**Abstract:** The basic reproduction number, $R_0$, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating this quantity from epidemic incidence data can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We show that by conditioning a `deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.

##### 1.Entropic contribution to phenotype fitness

**Authors:**Pablo Catalán, Juan Antonio García-Martín, Jacobo Aguirre, José A. Cuesta, Susanna Manrubia

**Abstract:** All possible phenotypes are not equally accessible to evolving populations. In fact, only phenotypes of large size, i.e. those resulting from many different genotypes, are found in populations of sequences, presumably because they are easier to discover and maintain. Genotypes that map to these phenotypes usually form mostly connected genotype networks that percolate the space of sequences, thus guaranteeing access to a large set of alternative phenotypes. Within a given environment, where specific phenotypic traits become relevant for adaptation, the replicative ability of a phenotype and its overall fitness (in competition experiments with alternative phenotypes) can be estimated. Two primary questions arise: how do phenotype size, reproductive capability and topology of the genotype network affect the fitness of a phenotype? And, assuming that evolution is only able to access large phenotypes, what is the range of unattainable fitness values? In order to address these questions, we quantify the adaptive advantage of phenotypes of varying size and spectral radius in a two-peak landscape. We derive analytical relationships between the three variables (size, topology, and replicative ability) which are then tested through analysis of genotype-phenotype maps and simulations of population dynamics on such maps. Finally, we analytically show that the fraction of attainable phenotypes decreases with the length of the genotype, though its absolute number increases. The fact that most phenotypes are not visible to evolution very likely forbids the attainment of the highest peak in the landscape. Nevertheless, our results indicate that the relative fitness loss due to this limited accessibility is largely inconsequential for adaptation.

##### 2.Statistical measures of complexity applied to ecological networks

**Authors:**Claudia Huaylla, Marcelo N Kuperman, Lucas A. Garibaldi

**Abstract:** Networks are a convenient way to represent many interactions among different entities as they provide an efficient and clear methodology to evaluate and organize relevant data. While there are many features for characterizing networks there is a quantity that seems rather elusive: Complexity. The quantification of the complexity of networks is nowadays a fundamental problem. Here, we present a novel tool for identifying the complexity of ecological networks. We compare the behavior of two relevant indices of complexity: K-complexity and Single value decomposition (SVD) entropy. For that, we use real data and null models. Both null models consist of randomized networks built by swapping a controlled number of links of the original ones. We analyze 23 plant-pollinator and 19 host-parasite networks as case studies. Our results show interesting features in the behavior for the K-complexity and SVD entropy with clear differences between pollinator-plant and host-parasite networks, especially when the degree distribution is not preserved. Although SVD entropy has been widely used to characterize network complexity, our analyses show that K-complexity is a more reliable tool. Additionally, we show that degree distribution and density are important drivers of network complexity and should be accounted for in future studies.